Try United Road. They do west coast shipping and they farm out to insured and bonded truckers.
I dealt with them and it all worked out fine.
They have a great reputation and track record, so I would not be concerned if they farm out your vehicle to a legit trucker going east.
Do not do business with an auto shipping company called Cross Country.
They are amature, non-porfessional, will not commit to a pick-up date, nor a delivery date. Slackers from every angle! Stay away!!
p.s. I and I assume most forum members would agree "don't let a stranger drive your ride!" You will never know what was done, nor how it was driven, but the mechanic will when you pay the bill.
Good luck with shipping your vehicle.